Out-of-time-ordered density correlators in Luttinger liquids

TL;DR

This paper investigates out-of-time-ordered density correlators in Luttinger liquids, revealing universal and non-universal features of information scrambling, with implications for understanding quantum chaos in strongly correlated systems.

Contribution

It demonstrates the behavior of OTO density correlators in Luttinger liquids, including universal growth patterns and the impact of interactions, supported by numerical benchmarks.

Findings

OTOC commutators grow as t^2 at short times

Universal temperature and initial state independence observed

Persistence of key features in non-integrable models

Abstract

Information scrambling and the butterfly effect in chaotic quantum systems can be diagnosed by out-of-time-ordered (OTO) commutators through an exponential growth and large late time value. We show that the latter feature shows up in a strongly correlated many-body system, a Luttinger liquid, whose density fluctuations we study at long and short wavelengths, both in equilibrium and after a quantum quench. We find rich behaviour combining robustly universal and non-universal features. The OTO commutators display temperature and initial state independent behaviour, and grow as $t^2$ for short times. For the short wavelength density operator, they reach a sizeable value after the light cone only in an interacting Luttinger liquid, where the bare excitations break up into collective modes. We benchmark our findings numerically on an interacting spinless fermion model in 1D, and find persistence of central features even in the non-integrable case. As a non-universal feature, the short time growth exhibits a distance dependent power.